Introduction
First off, I apologize if this thread is a repeat of one someone else did. I did a quick search and found some related topics, but not really the same thing, so I thought it worthy of its own thread.
To give some background into why I did all this, I started looking into healing efficiency when two of the paladins in our guild received 4-piece Tier5. This has also come up again because of the choice between T6 and T5. Healing used to be straight-forward for me as a priest (you heal for x for y amount of mana), but things have become complicated as a paladin (faster casting times, illumination and crit %, BoL, mana cost reduction on spells, less +healing on down-ranked spells, spell haste, etc), and I thought it would be interesting to do the math and just see what paladin healing spells are most efficient.
The Goal
Find what ranks of Holy Light (HL) and Flash of Light (FL) are most efficient with different gear and how that efficiency scales with crit% and +healing.
Conclusions
Buffs and Gear
Blessing of Light (BoL) makes a significant difference to the efficiency of the lower ranks of HL. This is because BoL adds a flat bonus to all ranks of HL, which is a proportionately larger bonus at lower ranks. The Libram of Absolute Truth improves efficiency much more than the Libram of Souls Redeemed. The 4-Piece T5 paladin bonus makes HL cast 0.25s faster. These buffs and gear make HL4 a superior spell than FL7 in most regards.
Small Heals
If BoL is not on the target, FL7 is the best small heal to use. However, with BoL and some specific gear, HL4 becomes the most efficient small-heal spell in the paladin arsenal. HL4 also provides the additional benefit of keeping Light’s Grace active for times when your biggest heals are necessary.
Big Heals
Assuming the Libram of Absolute Truth is equipped along with the other stipulations: HL9 provides about 2.5x the healing/s of HL4 and is almost as efficient as HL7. HL11 provides about 3x the healing/s of HL4 and is the least efficient HL spell.
Scaling
Paladin healing spells scale linearly with +healing, but increase in efficiency faster with higher levels of crit %. Once a certain level of +healing is reached, paladins should aim for more crit % to improve healing/s and healing efficiency. Graphs that show this scaling are included in the spreadsheet.
The Setup
All of my calculations will be done assuming the following parameters are in play:
Buffs
Mana Restore (Insightful Earthstorm Diamond) = 300 mana on a spell cast with what I believe is an effective 2-3% chance proc rate.
Sancitified Light = 6% extra crit to HL
Light's Grace = -0.5 casting time for all HL spells cast in 15 seconds, proc'd when HL is cast
T5 4-piece = -0.25 casting time for HL
Healing Light = 12% extra healing on FoL and HL
- According to WoWWiki, this applies to both +healing and BoL (haven’t tested myself)
Equations
+healing to a max ranked spell: +healing_max_rank = cast time/3.5 * +healing
+healing for downranked spells: +healing_spell = ((level of spell + 5)/player level) * +healing_max_rank
Healing Done by a spell: Heal Average = (Spell Base + Blessing of Light + +healing_spell) * (Healing Light)
Gear/Buff Scenarios
(A) no extra modifiers
(B) Blessing of Light
(C) [Libram of Souls Redeemed] + BoL
(D) [Libram of Absolute Truth] + BoL
Assumptions
I’m going to use my gear for a base +healing of 2000, a base holy crit of 20%, and spell haste rating of 120 for the initial calculations and comparisons for each of the scenarios. I will also post some graphs for the last scenario (D) that show how the efficiency changes as +healing and crit% are scaled.
I will also assume that the down-ranking modifier is applied after the normal +healing calculation for the spell (i.e. they're multiplicative instead of additive).
The Calculations
Here is an example (for HL6) of how the calculations are performed to derive the healing/s, mana/s, and healing/mana numbers. These calculations are made in the same way for all of the ranks of HL and FL discussed, so there is no need to show the calculations for each rank.
Base spell stats:
HL6 - level 38: 364 mana, 698 to 780 healing
Cast-time modifier:
HL is base 2.5 seconds casting time, so this reduces the +healing gained:
HL: 2.5/3.5 * 2000 = 71.4% * 2000 = 1428
Level-Modifier:
((38+5)/70) * +healing = 61.4% * 1428 = 877 +healing
Adding it all up- (Base Spell, + healing bonus) * Healing Light Bonus (12% extra healing):
1764 to 1855 healing
If we cast 100 spells and assume a perfect world (i.e. you’ll get 29 crits with a 29% crit percentage):
2 of those should have 300 mana back (from Mana Restore) = 600 mana
26 will be crits with 1.5x healing and 60% mana back = 218 mana a piece
So total we will be doing:
(1764*74) + (1764*1.5)*26 = 199332 min healing
(1855*74) + (1855*1.5)*26 = 209615 max healing
In this amount of time (remember, 120 spell haste):
100 * 1.61 seconds = 161 seconds (2.68 minutes)
And we will have received back this amount of mana:
26 * 218 + 600 = 6268 mana
199332 to 209615 healing over 161 seconds = 1238 to 1301 healing/s
Total mana spent = 364*100 – 6268 = 30132 mana = 187 mana/s
Final Values:
1238 to 1301 healing/s
187 mana/s
1238/187 = 6.62 healing/mana min
1301/187 = 6.96 healing/mana max
Example Spreadsheet Results
Scenario (D): +2000 healing and 20% crit with BoL and Libram of Absolute Truth:
HL4: 1131 – 1167 healing/s, 79 mana/s,
14.54 average healing/mana
HL5: 1403 – 1451 healing/s, 123 mana/s, 11.60 average healing/mana
HL6: 1693 – 1758 healing/s, 170 mana/s, 10.15 average healing/mana
HL7: 2015 – 2100 healing/s, 223 mana/s, 9.23 average healing/mana
HL8: 2380 – 2492 healing/s, 283 mana/s, 8.61 average healing/mana
HL9: 2747 – 2889 healing/s, 325 mana/s, 8.67 average healing/mana
HL10: 2897 – 3053 healing/s, 351 mana/s, 8.48 average healing/mana
HL11: 3304 – 3500 healing/s, 419 mana/s, 8.12 average healing/mana
FL4: 785 – 805 healing/s, 48 mana/s, 16.56 average healing/mana
FL5: 924 – 949 healing/s, 63 mana/s, 14.87 average healing/mana
FL6: 1066 – 1099 healing/s, 78 mana/s, 13.88 average healing/mana
FL7: 1223 – 1267 healing/s, 101 mana/s,
12.33 average healing/mana
Final Note
Please have a look at the spreadsheet and play around with it. All you have to do is put in a few values in the blue boxes (+healing, crit%, and spell haste), and everything else should calculate out for you.
Let me know if you see any errors or anything I’ve left out and I’ll get it fixed as soon as I can.
I haven’t taken a look, yet, at T6 bonuses versus T5 and whether the crit on HL and extra healing on FoL make things more/less efficient than the T5 bonuses.
Spreadsheet
Spreadsheet can be found here:
Pally_Healing_Efficiency_v1.xls